Lean migration: Phase 7 (Sign + Constant analyses, executable)

- Spa.Showable: port of Showable.agda (quoted strings, map format) for
  output parity
- Spa.Analysis.Utils: eval_combine₂
- Spa.Lattice.AboveBelow.le_cases: order of the flat lattice by cases
- Spa.Analysis.Sign / Spa.Analysis.Constant: the four monotonicity
  POSTULATES from the Agda files are now proved theorems (via le_cases);
  interpretations, evaluator validity, analyze_correct per analysis
- Main + lake exe spa: runs both analyses on the Agda test program;
  constant analysis folds unknown=0, sign analysis gives unknown=⊤

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

lean/Spa/Lattice/AboveBelow.lean

@@ -134,6 +134,27 @@ theorem mk_lt_top (x : α) : (mk x : AboveBelow α) < top :=
 theorem bot_lt_top : (bot : AboveBelow α) < top :=
   lt_of_le_of_ne (bot_le' _) (by simp)
 
+/-- The order of the flat lattice, by cases (used to discharge the
+monotonicity obligations that were `postulate`d in `Analysis/Sign.agda` and
+`Analysis/Constant.agda`). -/
+theorem le_cases {a b : AboveBelow α} (h : a ≤ b) :
+    a = bot ∨ b = top ∨ a = b := by
+  have hsup := le_iff.mp h
+  rcases a with _ | _ | x <;> rcases b with _ | _ | y
+  · exact Or.inl rfl
+  · exact Or.inr (Or.inl rfl)
+  · exact Or.inl rfl
+  · exact absurd hsup (by simp)
+  · exact Or.inr (Or.inl rfl)
+  · exact absurd hsup (by simp)
+  · exact absurd hsup (by simp)
+  · exact Or.inr (Or.inl rfl)
+  · rw [mk_sup_mk] at hsup
+    by_cases hxy : x = y
+    · exact Or.inr (Or.inr (by rw [hxy]))
+    · rw [if_neg hxy] at hsup
+      exact absurd hsup (by simp)
+
 /-- Rank of an element: `⊥ ↦ 0`, `[x] ↦ 1`, `⊤ ↦ 2`. Used to bound chains
 (Agda's `isLongest` / `x≺[y]⇒x≡⊥` / `[x]≺y⇒y≡⊤` case analysis lives here). -/
 def rank : AboveBelow α → ℕ